Probing superhydrophobic surface topography using droplet adhesion

Abstract

Understanding contact line dynamics on superhydrophobic surfaces with microscopic structures is essential for designing materials with reduced drag, anti-icing, self-cleaning, and anti-fouling properties. Using numerical simulations, we demonstrate that forces on droplets receding over structured surfaces are governed by microscale deformations near the contact line. We present and experimentally validate an expression demonstrating that adhesion force increases logarithmically with pillar area fraction at constant droplet volume and pillar surface chemistry. Furthermore, we establish that the average tensile force measured in direct force measurements provides a more reliable indicator of surface structure than the commonly used maximum force. This newfound insight enables precise quantification of superhydrophobic surface structure using a droplet probe.

Figures (8)

• Figure 1: Simulation of the recede stage for a droplet ($V = 1.6$$\mu$L, $\theta_{\rm{A}} = 111.2$°, $\theta_{\rm{R}} = 98.7)$° on a superhydrophobic surface with $\phi = 0.015$, showing the (a) corresponding liquid-air interface equilibrium states and variation of (b) Laplace pressure ($\Delta p$), (c) contact angle ($\theta_{\rm{m}}$), (d) net vertical force $F$, (e) droplet base radius ($R$), and (f) apparent CL. Points $i,iii,v,vii$ and $ii, iv, vi$ and $viii$ represent the equilibrium states just before and after the CL executes a jump, respectively. Solid black and red lines in (a) and (f) represent the first and the second critical states respectively. The dashed black lines in (a) represent the droplet profile when the CL is pinned on a set of pillars before executing jump $i \rightarrow ii$. Points $iii$ and $iv$ are not shown in (a) as the jump $iii \rightarrow iv$ occurs out of the plane. The droplet base radius and macroscopic contact angle are calculated at the apparent CL shown in (f) at 20 $\mu$m above the pillar tops.
• Figure 2: (a) Droplet morphology depicting one of the equilibrium states during a typical recede stage for volume $V = 1.6$$\mu$L, $\theta_{\rm{A}} = 111.2$°, $\theta_{\rm{R}} = 98.7$° on a superhydrophobic surface with $\phi = 0.05$. The CL at $\Delta z=1$$\mu$m and 20 $\mu$m from pillar tops, respectively are shown in blue and black. (b) Macroscopic contact angle variation ($\theta_{\rm{m}}$) measured at different $\Delta z$ relative to the viewing direction ($\psi$) with respect to the $x$ axis. (c) Apparent CL at $\Delta z=1,5,10$ and 20 $\mu$m are shown in blue, red, green and black respectively. (d) Droplet footprint area as a function of $\Delta z$. The area is estimated considering a circular CL based on the base radius measured along the $x$ axis ($\psi=0$°) and at 45° to the $x$ axis are shown as filled triangles and circles respectively. The variation in the area based on the averaged base radius is also shown as filled squares. The results shown are for $\phi=0.05$.
• Figure 3: Apparent CL ($\Delta z=1$$\mu$m) at different times during recede stage for a droplet of volume $V = 1.6$$\mu$L, $\theta_{\rm{A}} = 111.2$°, $\theta_{\rm{R}} = 98.7$° on a superhydrophobic surface with $\phi = 0.05$ ($t_4>t_3>t_2>t_1>t_0$). (b) Liquid-air interface in the plane corresponding to the $X-X$ section in (a).
• Figure 4: Variation in the maximum adhesion force ($F_{\rm{max}}$) and average tensile force ($F_{\rm{avg}}$) with pillar area fraction ($\phi$) based on numerical simulations and physical experiments, for a droplet volume $V = 1.6$$\mu$L, $\theta_{\rm{A}} = 111.2$°, $\theta_{\rm{R}} = 98.7$° and $d=10$$\mu$m, are shown by filled and empty symbols respectively. Eq. (\ref{['eqn:non_dilute_fit']}) using the numerically predicted values of the parameters $a,b,c$ are also shown as black and red curves for $F_{\rm{max}}$ ($a=331.8,b=-756.3,c=400.5$) and $F_{\rm{avg}}$ ($a=209.1,b=-458.7,c=253.2$) respectively.
• Figure 5: Variation in the pressure ($F_{\rm{p}}$), surface tension ($F_{\sigma}$) and total force ($F=F_{\rm{p}}+F_{\sigma}$) with time (t) in simulation units. The simulations were performed for a droplet volume $V=1.6$$\mu$L, $\theta_{\rm{A}}=111.2$° and $\theta_{\rm{R}}=98.7$° on a superhydrophobic surface with $\phi=0.05$.